基于最大化期望的多目标设计

发布时间：2018-06-21 12:10

本文选题：克里金法 + 多目标　；参考：《清华大学》2015年硕士论文

【摘要】：超材料可以达到单一材料无法达到的电磁学性质故而受到广泛关注。然而超材料的设计常常涉及其中大量微元件的设计,这些设计只能通过费时的计算机实验得到,本文针对超材料设计中遇到的一类多目标问题提出新的方法,以减少最终所需的计算机实验次数。在现实中经常会遇到给定函数值求解自变量的问题,通常函数的反函数是没有解析表达式甚至未知的,函数本身的计算也需要花费很大的时间成本。通常使用代理模型,如克里金模型,预测函数值来减少和规避真实函数本身的计算。很多文献研究了使用代理模型对单目标函数和多个目标函数的实验设计问题,然而在我们的问题中,响应函数相同而响应的目标值很多,并不符合过去多目标的情形。为了减少时间和实验次数,本文使用克里金法对超材料设计中的真实实验数据建立代理模型并检验了精度,对于单一函数的多目标问题提出新的设计方法,使用Branin函数测试的结果也显示出相比于对于每个目标单独地使用EGO,新方法所需的实验次数更少且更加稳定。
[Abstract]:The electromagnetic properties of metamaterials which can not be achieved by a single material have attracted wide attention. However, the design of metamaterials often involves the design of a large number of microelements, which can only be obtained through time-consuming computer experiments. In this paper, a new method is proposed for a class of multi-objective problems encountered in the design of metamaterials. To reduce the number of computer experiments that are ultimately required. In reality, we often encounter the problem of solving independent variables with given function values. Usually, the inverse function of a function does not have an analytic expression or even an unknown one, and the calculation of the function itself takes a lot of time cost. The proxy model, such as Kriging model, is usually used to predict the value of the function to reduce and avoid the calculation of the real function itself. Many literatures have studied the experimental design problem of single-objective function and multi-objective function using agent model. However, in our problem, the response function is the same and the target value of response is many, which does not accord with the situation of multi-objective in the past. In order to reduce the time and the number of experiments, this paper uses Kriging method to establish a proxy model for the real experimental data in the design of metamaterials and to test the accuracy. A new design method is proposed for the multi-objective problem of a single function. The test results using the Branin function also show that the new method requires fewer and more stable experiments than using EGO for each target alone.
【学位授予单位】：清华大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB34;O441

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